28 citations · 31 across the 8 of their papers we have counts for
4 papers · 1 filter
Morse predecomposition of an ivariant set
Michał Lipiński, Konstantin Mischaikow, Marian Mrozek
Motivated by the study of the recurrent orbits in a Morse set of a Morse decomposition, we introduce the concept of Morse predecomposition of an isolated invariant set in the setti…
The poset of cancellations induced by gradient dynamics in a filtered Lefschetz complex
Herbert Edelsbrunner, Michał Lipiński, Marian Mrozek +1
Motivated by questions about simplification of topology, we take a discrete approach to the dependency of simplifying operations, using methods based on combinatorial gradient dyna…
Computing Connection Matrices via Persistence-like Reductions
Tamal K. Dey, Michał Lipiński, Marian Mrozek +1
Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for…
Testing topological conjugacy of time series
Paweł Dłotko, Michał Lipiński, Justyna Signerska-Rynkowska
This paper considers a problem of testing, from a finite sample, a topological conjugacy of two dynamical systems and . More precisely, given $x_1,\ldots, x_n \subse…